Algebraic automata theory, that is, the use of algebraic tools and notions such as
monoids, morphisms and varieties, has been very successful in classifying recognizable
word languages, from both the theoretical and the algorithmic points of view, offering
structural descriptions of, say, logically defined classes of languages and decision
algorithms for membership in these classes
[1]}, [2]}, [3]}. The purpose of this paper is to
extend some of this approach to the concurrent setting. We are particularly interested in
decomposition results, in the spirit of the Krohn-Rhodes theorem, and their applications
to the study of first-order definable trace languages.
